The Harmony Search algorithm with additional improvement of harmony memory for Asymmetric Traveling Salesman Problem

This paper presents a modification of the Harmony Search algorithm (HS) adjusted to an effective solving of instances of the Asymmetric Traveling Salesman Problem. The improvement of the technique spans the application of a pheromone, which, by serving the role of long-term memory, enables the improvement of the quality of determined results, especially for tasks characterized by a significant number of vertices. The publication includes the results of tests that suggest the achievement of effectiveness improvement through the modification of the HS and recommendations concerning the proper configuration of the algorithm.

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Modified Harmony Search Algorithm for 0-1 Knapsack Problems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.365-366.182 ◽

2013 ◽

Vol 365-366 ◽

pp. 182-185

Author(s):

Hong Gang Xia ◽

Qing Liang Wang

Keyword(s):

Convergence Rate ◽

Objective Function ◽

Objective Function Value ◽

Search Algorithm ◽

Harmony Search ◽

Harmony Search Algorithm ◽

Knapsack Problems ◽

Convergence And Stability ◽

Update Strategy ◽

Harmony Memory

In this paper, a modified harmony search (MHS) algorithm was presented for solving 0-1 knapsack problems. MHS employs position update strategy for generating new solution vectors that enhances accuracy and convergence rate of harmony search (HS) algorithm. Besides, the harmony memory consideration rate (HMCR) is dynamically adapted to the changing of objective function value in the current harmony memory, and the key parameters PAR and BW dynamically adjusted with the number of generation. Based on the experiment of solving ten classic 0-1 knapsack problems, the MHS has demonstrated stronger convergence and stability than original harmony search (HS) algorithm and its two improved algorithms (IHS and NGHS).

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The Lot-Streaming Flow Scheduling Shops Based on a Hybrid Discrete Harmony Search Algorithm

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.204-210.563 ◽

2011 ◽

Vol 204-210 ◽

pp. 563-568

Author(s):

Hong Yan Han

Keyword(s):

Flow Shop ◽

Search Algorithm ◽

Harmony Search ◽

Harmony Search Algorithm ◽

Flow Shop Scheduling ◽

Neighborhood Search ◽

Lot Streaming ◽

Discrete Harmony Search ◽

Harmony Memory ◽

Streaming Flow

To solve the lot-streaming flow shop scheduling problem with the objective to minimize the total weighted earliness and tardiness, a hybrid discrete harmony search (HDHS) algorithm is proposed in this paper. Firstly, an effective harmony memory initialization approach is presented,an initial solution in harmony memory is generated by means of the famous NEH heuristic. Secondly, the HDHS algorithm utilizes an effective improvisation mechanism to generate new harmonies represented by job permutations. Lastly, the insert neighborhood search and swap operator are designed and embedded in the algorithm to enhance the local exploitation.Experimental results demonstrate the effectiveness of the proposed HDHS algorithms.

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A Modified Harmony Search Algorithm for Numerical Optimization Problems

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.989-994.2532 ◽

2014 ◽

Vol 989-994 ◽

pp. 2532-2535

Author(s):

Hong Gang Xia ◽

Qing Zhou Wang

Keyword(s):

Numerical Optimization ◽

Learning Strategy ◽

Optimization Problems ◽

Objective Function Value ◽

Search Algorithm ◽

Harmony Search ◽

Harmony Search Algorithm ◽

The Other ◽

Self Learning ◽

Harmony Memory

This paper presents a modified harmony search (MHS) algorithm for solving numerical optimization problems. MHS employs a novel self-learning strategy for generating new solution vectors that enhances accuracy and convergence rate of harmony search (HS) algorithm. In the proposed MHS algorithm, the harmony memory consideration rate (HMCR) is dynamically adapted to the changing of objective function value in the current harmony memory. The other two key parameters PAR and bw adjust dynamically with generation number. Based on a large number of experiments, MHS has demonstrated stronger convergence and stability than original harmony search (HS) algorithm and its two improved algorithms (IHS and GHS).

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A Reward Population-Based Differential Genetic Harmony Search Algorithm

Algorithms ◽

10.3390/a15010023 ◽

2022 ◽

Vol 15 (1) ◽

pp. 23

Author(s):

Yang Zhang ◽

Jiacheng Li ◽

Lei Li

Keyword(s):

Search Algorithm ◽

Harmony Search ◽

Memory Search ◽

Population Based ◽

Harmony Search Algorithm ◽

Global Search ◽

Calculation Results ◽

Optimal Average ◽

Average Fitness ◽

Harmony Memory

To overcome the shortcomings of the harmony search algorithm, such as its slow convergence rate and poor global search ability, a reward population-based differential genetic harmony search algorithm is proposed. In this algorithm, a population is divided into four ordinary sub-populations and one reward sub-population, for each of which the evolution strategy of the differential genetic harmony search is used. After the evolution, the population with the optimal average fitness is combined with the reward population to produce a new reward population. During an experiment, tests were conducted first on determining the value of the harmony memory size (HMS) and the harmony memory consideration rate (HMCR), followed by an analysis of the effect of their values on the performance of the proposed algorithm. Then, six benchmark functions were selected for the experiment, and a comparison was made on the calculation results of the standard harmony memory search algorithm, reward population harmony search algorithm, differential genetic harmony algorithm, and reward population-based differential genetic harmony search algorithm. The result suggests that the reward population-based differential genetic harmony search algorithm has the merits of a strong global search ability, high solving accuracy, and satisfactory stability.

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A Cooperative Harmony Search Algorithm for Function Optimization

Mathematical Problems in Engineering ◽

10.1155/2014/587820 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Gang Li ◽

Qingzhong Wang

Keyword(s):

Optimization Problems ◽

Search Algorithm ◽

Cooperative Behavior ◽

Optimization Technique ◽

Harmony Search ◽

Harmony Search Algorithm ◽

Function Optimization ◽

Solution Vector ◽

Original Algorithm ◽

Harmony Memory

Harmony search algorithm (HS) is a new metaheuristic algorithm which is inspired by a process involving musical improvisation. HS is a stochastic optimization technique that is similar to genetic algorithms (GAs) and particle swarm optimizers (PSOs). It has been widely applied in order to solve many complex optimization problems, including continuous and discrete problems, such as structure design, and function optimization. A cooperative harmony search algorithm (CHS) is developed in this paper, with cooperative behavior being employed as a significant improvement to the performance of the original algorithm. Standard HS just uses one harmony memory and all the variables of the object function are improvised within the harmony memory, while the proposed algorithm CHS uses multiple harmony memories, so that each harmony memory can optimize different components of the solution vector. The CHS was then applied to function optimization problems. The results of the experiment show that CHS is capable of finding better solutions when compared to HS and a number of other algorithms, especially in high-dimensional problems.

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Opposition-Based Improved Harmony Search Algorithm Solve Unconstrained Optimization Problems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.365-366.170 ◽

2013 ◽

Vol 365-366 ◽

pp. 170-173

Author(s):

Hong Gang Xia ◽

Qing Zhou Wang ◽

Li Qun Gao

Keyword(s):

Optimization Problems ◽

Search Algorithm ◽

Harmony Search ◽

Continuous Optimization ◽

Search Space ◽

Harmony Search Algorithm ◽

Solution Quality ◽

Improved Harmony Search ◽

Improved Harmony Search Algorithm ◽

Harmony Memory

This paper develops an opposition-based improved harmony search algorithm (OIHS) for solving global continuous optimization problems. The proposed method is different from the classical harmony search (HS) in three aspects. Firstly, the candidate harmony is randomly chosen from the harmony memory or opposition harmony memory was generated by opposition-based learning, which enlarged the algorithm search space. Secondly, two key control parameters, pitch adjustment rate (PAR) and bandwidth distance (bw), are adjusted dynamically with respect to the evolution of the search process. Numerical results demonstrate that the proposed algorithm performs much better than the existing HS variants in terms of the solution quality and the stability.

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An Improved Harmony Search Algorithm with Application

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.687-691.1367 ◽

2014 ◽

Vol 687-691 ◽

pp. 1367-1372

Author(s):

Jian Ping Li ◽

Ai Ping Lu ◽

Hao Chang Wang ◽

Xin Li ◽

Pan Chi Li

Keyword(s):

Population Size ◽

Search Algorithm ◽

Harmony Search ◽

Optimal Solution ◽

Harmony Search Algorithm ◽

Global Optimal Solution ◽

Improved Harmony Search ◽

Global Optimal ◽

Improved Harmony Search Algorithm ◽

Harmony Memory

In classical harmony search algorithm, only one harmony vector is obtained in each of iteration, which affects its search ability. We propose an improve harmony search algorithm in this paper. In our approach, the number of harmony vectors obtained in each of iteration is equivalent to the population size, and all newly generated harmony vectors are put into the harmony memory array. Then, all harmony vectors are sorted by descending order of the fitness, and the first half individuals are served as the next generation of populations. Experimental results show that our approach is obviously superior to the classical one under the same iteration steps and the same running time, which reveals that our approach can effectively generate the excellent individuals approximating the global optimal solution and enhance the optimization ability of classical harmony search algorithm.

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